Lately there was a growing interest in studying self-similarity and fractal
properties of graphs, which is largely inspired by applications in biology, sociology and chemistry [1]}, [2]}. Such studies often employ
statistical physics methods that use ideas from graph theory and general topology, but are not intended to approach the problems under consideration in a rigorous mathematical way. Several studies that translate certain notions of topological dimension theory to graphs using combinatorial methods are also known [3]}, [4]}. However, to the best of our knowledge a rigorous combinatorial theory that defines and studies graph-theoretical analogues of topological fractals still has not been developed.
